Kernel density estimation is a non-parametric method to estimate an
unknown probability density function (PDF) using a sample
set. Although many other non-parametric methods exist, such as
histograms or frequency polygons, KDE has the advantage that it is
independent of the bin size and the starting bin, and that it produces
a smooth estimate of the PDF, allowing for a better representation of
multimodality [1]}. In KDE, the goodness of
the PDF estimation depends crucially on two concepts: the chosen
kernel function and the bandwidth size. Multivariate kernel density
estimation is the extension of KDE to higher dimensions, when the
joint probability distribution of a set of variables must be
estimated. On the other hand, adaptive KDE refers to the possibility
of using a different smoothing parameter in different regions of the
PDF domain. The name KDE will refer to all variants of the kernel
density estimation method throughout this work.
